On structure-oriented hybrid two-stage iteration methods for the large and sparse blocked system of linear equations

Authors:
Yi Zheng;Wenbin Guo;Jianli Zhao;Nan Wang
Affiliations:
School of Mathematics Science, Liaocheng University, Shandong, 252059, China;School of Mathematics Science, Liaocheng University, Shandong, 252059, China;School of Mathematics Science, Liaocheng University, Shandong, 252059, China;School of Mathematics Science, Liaocheng University, Shandong, 252059, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 8
Cited 0

Two-stage and multisplitting methods for the parallel solution of linear systems

SIAM Journal on Matrix Analysis and Applications
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems

SIAM Journal on Numerical Analysis
A class of parallel hybrid two-stage iteration methods for block bordered linear systems

Applied Mathematics and Computation
Uzawa type algorithms for nonsymmetric saddle point problems

Mathematics of Computation
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems

SIAM Journal on Matrix Analysis and Applications
A Preconditioner for Generalized Saddle Point Problems

SIAM Journal on Matrix Analysis and Applications
Fast QR Eigenvalue Algorithms for Hessenberg Matrices Which Are Rank-One Perturbations of Unitary Matrices

SIAM Journal on Matrix Analysis and Applications
Eigenvalues and Jordan canonical form of a successively rank-one updated complex matrix with applications to Google's PageRank problem

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper, we first present a class of structure-oriented hybrid two-stage iteration methods for solving the large and sparse blocked system of linear equations, as well as the saddle point problem as a special case. And the new methods converge to the solution under suitable restrictions, for instance, when the coefficient matrix is positive stable matrix generally. Numerical experiments for a model generalized saddle point problem are given, and the results show that our new methods are feasible and efficient, and converge faster than the Classical Uzawa Method.